Abstract:
"Bit" is a contraction of "binary digit," but unlike a classical bit, which is plain-vanilla binary with a value of either 0 or 1, a quantum bit, or qubit -- the theoretical basis of quantum computing -- holds both 0 and 1 in a superposed state until it is measured.

A vast computational space can be created with relatively few quantum-mechanically entangled qubits, and the measurement of one qubit can instantly resolve an intricate calculation when all the entangled qubits are "collapsed" to a specific value by the measurement.

So how does one make and measure a qubit? The problem has engaged scientists for years. Many arrangements have been proposed and some demonstrated, each with its advantages and disadvantages, including tricky schemes involving superconducting tunnel junctions, quantum dots, neutral atoms in optical lattices, trapped ions probed by lasers, and so on.

In the long run, however, qubits based on individual dopant atoms implanted in silicon may have the edge. The materials and methods of silicon-chip manufacturing are familiar and, when applied to quantum-computer devices, have the potential for easy scale-up.

A Toolkit for Silicon-Based Quantum Computing

Berkeley, CA | Posted on October 23rd, 2008

"There are three pillars to the development program my colleagues and I have been following," says Thomas Schenkel of Berkeley Lab's Accelerator and Fusion Research Division. "One is the theory of quantum measurement in the devices we build, led by Professor Birgitta Whaley from the Department of Chemistry at UC Berkeley; another is the fabrication of these devices, headed by myself and Professor Jeff Bokor from UC Berkeley's Department of Electrical Engineering and Computer Science; and the third is to actually measure quantum states in these devices, an effort led by Professor Steve Lyon from Princeton's Department of Electrical Engineering. Of course, things don't necessarily happen in that order."

In fact, long before Schenkel and his colleagues learned how to perform measurements at scales approaching that of single atoms -- or even understood the theory behind their measurements -- they had already made great strides toward building practical single-atom electronic devices of the kind essential to embody qubits in silicon.

Such devices may make a major contribution not only to quantum computing but to the entire emerging field of spintronics, the advanced form of electronics that makes use not only of electron charge but of electron spin as well -- the quantum property of electrons by which they behave as tiny bar magnets.

A single-atom injector

The sine qua non of qubits in silicon is the ability to plant one atom at a time where it's wanted. In his lab in one of the more venerable buildings at Berkeley Lab, Schenkel and his students have used a focused ion beam to implant single ions in devices mere millionths of a meter square. (An ion is an atom with net charge, typically lacking one or more electrons.)

"Single-atom effects have been observed before, but the yields are so low as to be impractical -- or the devices are randomly formed, with no control or predictability," Schenkel says. "Our approach to single-atom doping integrates ion beams with a modified scanning force microscope. We use the microscope's cantilever tip for both the nondestructive imaging of the target area and to position the ion beam."

The device has the advantage of using virtually any species of atoms, says Schenkel. "We can start with any source of neutral atoms, such as phosphorus or antimony -- manganese is fashionable right now -- and choose one of a number of different sources to ionize them."

The low-energy focused ion beam is sent through a hole in the microscope's cantilever. "The hole in the tip acts as a tiny aperture or mask," says Schenkel. "We've demonstrated holes with diameters as small as five nanometers" -- five billionths of a meter.

To confirm that an ion has been implanted in the silicon, the region is fitted with electrodes to form a transistor channel, placed under a bias voltage. Then the implantation of a single ion -- even in a target area as large as two micrometers on a side (two millionths of a meter) -- can be detected as a change in the resistance of the channel current. Schenkel compares the current to electrons sliding down a hill; the presence of an implanted ion, he says, "is a bump in the way -- it impedes the electron flow."

Says Schenkel, "The method is so sensitive that single-ion hits can be detected at room temperature in a device as large as four square microns. Inside that region we can form numerous single-atom devices, each with dimensions less than 100 nanometers." Before making a specific transistor or other device, single-ion implantation can be "practiced" with atoms of a noble gas that do not dope the substrate. "We wait until the transistor settles down, then switch to the species we want."

Measurement and theory

Once a suitable atom is implanted in a transistor, how can its spin state be read? The most influential paper to advocate quantum computing in silicon appeared in Nature in 1998; by Bruce Kane, now of the University of Maryland, it was titled "A silicon-based nuclear spin quantum computer" and proposed using the nuclear spins of phosphorus atoms as qubits.

An atom is characterized by more than one kind of spin, however. Nuclear spin gives rise to a weak but long-lasting signal, while the signal from electron spin is stronger but easily disrupted. The spin readout mechanism devised and recently demonstrated by Schenkel and his colleagues, called spin-dependent scattering -- and based in turn on a technique known as "electrically detected magnetic resonance" -- makes use of both the nuclear and electron kinds of spin.

First a qubit is encoded in the dopant atom's electron spin state by zapping it with radio waves. Unfortunately any subsequent attempt to measure this spin directly (Schenkel's device detects spin states by using the interaction of the dopant atom's electrons with the electrons that form the current in the transistor) would destroy the information.

Luckily, however, the electron spin is firmly linked to the nuclear spin, and the electron spin state can be transferred to the nucleus. Like electrons, nuclei with an odd number of protons and neutrons (including phosphorus and antimony) also act as tiny bar magnets and, in a constant magnetic field, align themselves "up" or "down" (typically a few more ups than downs, because ups require less energy). And like electrons, the spinning nuclei can be induced to flip by a resonant field, although at a different (microwave) frequency.

By first turning off the transistor current, next zapping the electrons with microwaves, and then zapping the nucleus with radio-frequency waves, the electron spin is transferred to the nucleus and the qubit is set. In this way spin-coherence time is lengthened, the time during which this qubit may remain entangled with others in the computer.

When the readout current is turned on, the electron spins deteriorate. But nuclear spin orientations are still distinguishable in the atom's spectrum: electrons that would otherwise have the same energy react differently with the magnetic field, and the spectral lines of electrons surrounding a spin-up nucleus split in different ways from those surrounding a spin-down nucleus. This difference can be read from the resistance in the transistor's channel current -- thus, "electrically detected magnetic resonance."

Electrically detected magnetic resonance was first demonstrated by Ruby Ghosh, now of Michigan State University, and Robert Silsbee of Cornell University in 1992, using large-area transistors and measuring the signal from hundreds of millions of phosphorus atoms; their readouts were subject to substantial interference. Through constant refinements to the experimental set-up (and the choice of antimony over phosphorus), Schenkel and his colleagues have improved sensitivity 10,000 fold so far. The key ingredients in this progress have been the fabrication facilities of the UC Berkeley Microlab and Berkeley Lab's Molecular Foundry, as well as the close connection with Bokor and his UC Berkeley electrical engineering students.

While they have not yet been able to read the spin state of an individual atom, the technique is so sensitive that the path to the readout of single spin states in qubits seems open, a conclusion strongly supported by the measurement theory developed by Whaley's group. Here, detailed analysis of the measurement conditions in the transistors showed that encoding the electron spin information on the nuclear spin enables single-spin readout, while nevertheless preserving the spin-state information. The latter feature earns this scheme the label of "quantum nondemolition (QND) measurement of single spins in semiconductors."

This double-barreled readout mechanism -- encoding the electron spin, transferring that spin to the nucleus, then reading the original orientation from the effect of the nucleus on the atomic spectrum -- appears to offer significant advantages over other recent demonstrations of electron-spin readout alone.

To perform a crucial demonstration of coherent information transfer from electron to nuclear spins and back, Schenkel collaborated with colleagues John Morton of Oxford University, Steve Lyon of Princeton University, and Joel Ager of Berkeley Lab's Materials Sciences Division. Ager and his team removed silicon-29 isotopes from crystals of silicon-28 while maintaining high chemical purity. The isotopically enriched silicon-28 crystals provided a near-perfect environment for dopant atoms of phosphorus.

With ensembles of these atoms, as the researchers report in the October 23 issue of Nature, they were able to demonstrate a nuclear-spin memory time of a stunning 1.75 seconds.

"This is an extraordinarily long time to keep delicate quantum coherence intact," says Schenkel, "and it is this awesome stability, together with exquisite control over the spin degrees of freedom, that motivate our development of single-atom doping and single-spin readout-device development."

In sum, says Schenkel, "We have demonstrated a spin-readout mechanism in fully functional transistors, one that we believe is clean and -- although this remains to be seen -- well suited for integration of qubits. Our readout process is quantum nondemolition, so the spin is not switched in the readout process. And we have shown that the delicate quantum information can be stored for seconds. Finally, our single-ion placement technique can be used to dope any potential silicon-based quantum computer device with single atoms."

With the recent research of Schenkel and his colleagues, both experimental and theoretical, the toolkit for achieving the ultimate goal of scalable quantum computing in silicon is developing rapidly.

"Quantum non-demolition measurements of single donor spins in semiconductors," by Mohan Sarovar, Kevin C. Young, Thomas Schenkel, and K. Birgitta Whaley, is available online at arxiv.org/abs/0711.2343

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